Modified Adomian method for the generalized inhomogeneous Lane-Emden-type equations

The present study investigates certain singular Initial-Value Problems (IVPs) featuring the classical and generalized inhomogeneous Lane-Emden-type equations. These equations are very important models as they appear in many physical applications, including thermodynamics to mention a few. Further, the study proposes different forms of inverse integral operators that are based on the Adomian method to accelerate the convergence rate of the standard Adomian Decomposition Method (ADM). The method is then applied to various types of linear and nonlinear test problems and was found to be an effective modification by monitoring the rapidity of the convergence rate.